/sci/ - Science & Math

Euler is not amused

>>5876899
euler is laughing at you boy.

http://img11.hostingpics.net/pics/457397putnam002.gif

we want to prove: sin(A+B)/cos(A+B) = (tanA+tanB)/(1-tanA tanB)

put z = exp(iA), w = exp(iB) so zw = exp(i(A+B)) and

cos(A) = (z+1/z)/2
sin(A) = (z-1/z)/2i
tan(A) = -i(z-1/z)/(z+1/z)
cos(B) = (w+1/w)/2
sin(B) = (w-1/w)/2i
tan(B) = -i(w-1/w)/(w+1/w)
cos(A+B) = (zw+1/(zw))/2
sin(A+B) = (zw-1/(zw))/2i
tan(A+B) = -i(zw-1/(zw))/(zw+1/(zw))

so need to show -i(zw-1/(zw))/(zw+1/(zw)) = (-i(z-1/z)/(z+1/z) + -i(w-1/w)/(w+1/w))/(1 - ( -i(z-1/z)/(z+1/z))(-i(w-1/w)/(w+1/w)))

so check it in calculator PARI/gp

? -I*(z*w-1/(z*w))/(z*w+1/(z*w)) - (-I*(z-1/z)/(z+1/z) + -I*(w-1/w)/(w+1/w))/(1 - ( -I*(z-1/z)/(z+1/z))*(-I*(w-1/w)/(w+1/w)))
%1 = 0

proved.

Eulen? Is that what you call me these days you pussies?

Have you lost respect to me and all I represent to the extent that you are willing to make fun of my name and call me Eulen?

Fuck you all, I shouldn't have published any of my works for you pests to build on! I should have left you to figure math out for yourselves and fail, you sad fucks.

>>4757905
> Hard But possible
> Mfw there are more than two rooms with an odd number of doors.

homework? nigga I made the homework

It's there an Euler's algorithm for Greatest Common Divisor? I know the Euclidian Algorithm, but someone told me that there's an Euler algorithm... So far I only know that there could be a relationship with Euler's Phi Function, but in the function it's stablished that you know how to get GCD

Need help with some integration

f'(x)= 3(2x-1)^2

How do I integrate using the rule;

f(x)= 1/a*(f(x)^n+1)/n+1

When there is a coefficient in front of the brackets? I'm almost certain you don't expand. Any help please.

>>2671902
WHO AM I TALKING TO?? IS THAT YOU CARL?! YOU SANDBAGGING SON OF A BITCH!!!

-Leonhard

>>2253457
>Einstein
Bitch please, as for now no one wins with Euler. I still hope that one day Tao or other prodigy would top him.

Anyone in /sci/ doing problems on ProjectEuler.net?

I was wondering what language would be best to use to compute the answers and if an elegant algorithm was necessary since the computes are so powerful now. Maybe in 2001 when it started, you needed to optimize the code but wouldn't brute force just work now in 2010...

Your face when you come to /sci/ and you see "jsMath Loading".

>>1013242